Question

The sequence given is defined using a recursion formula. Write the first four terms of the sequence. a_1 =5 and a_n = 3a_n_1 + 3 for n > 2

Answer 1

The first four terms are:

`a_1=5,a_2=18,a_3=57,a_4=174`

Explanation:

When we define a sequence
`(a_n)` using a recursive formula, the k-th term of the sequence depends ont the previous k-1 terms, so we have to compute these first.

We are given that the first term is
`a_1=5`.

If your recursive formula holds for n>2 (excluding n=2), you need to define the second term beforehand. Since the second term is not given, the recursive formula must hold true for n≥2. Apply the formula with n=2 to get
`a_2=3a_(1)+3=3(5)+3=18`. Thus the second term is 18

Now, for n=3,
`a_3=3a_(2)+3=3(18)+3=57`. Hence the third term is 57.

For n=4,
`a_4=3a_(3)+3=3(57)+3=174`, then the fourth term is 174.